Question

question 6 of 10
louisa is purchasing a $125,000 home and her bank is offering her a 30-year mortgage at a 4.75% interest rate. in order to lower her monthly payment, louisa will make a 20% down payment and will purchase 2 points. what will her monthly mortgage payment be?

a. $506.69
b. $562.93
c. $545.98
d. $532.09

Explanation:

Step1: Calculate loan amount

Down payment = 20% of $125,000 = $25,000
Loan amount = $125,000 - $25,000 = $100,000

Step2: Adjust interest rate with points

1 point = 0.25% rate reduction
New rate = 4.75% - (2×0.25%) = 4.25% = 0.0425

Step3: Calculate monthly rate and periods

Monthly rate $r = \frac{0.0425}{12} ≈ 0.00354167$
Total periods $n = 30×12 = 360$

Step4: Compute monthly payment

Formula: $M = P×\frac{r(1+r)^n}{(1+r)^n - 1}$
$M = 100000×\frac{0.00354167(1+0.00354167)^{360}}{(1+0.00354167)^{360}-1} ≈ 506.69$

Answer:

A. $506.69